1. Field of the Invention
The present invention relates to an acoustic capacity, volume, and surface area measurement method which measures capacity, volume, and surface areas of complex-shaped containers or other objects using an acoustic technique.
2. Description of the Related Art
Conventionally known acoustic capacity measurement methods include one which involves giving alternating capacity changes to a reference vessel and a measuring vessel, measuring pressure changes in the vessels, finding acoustic impedance based on a ratio between the pressure changes, and thereby calculating capacity of the measuring vessel (see, for example, patent documents 1 and 2, the entire contents of which are hereby incorporated herein by reference).
Also known is an acoustic surface area measurement method which similarly measures a surface area of an object based on a phase difference of acoustic impedance (see, for example, patent document 3, the entire contents of which are hereby incorporated herein by reference).
According to this method, acoustic impedance Z in a closed space is given by Equations (1) to (3) below.
[Formula 1]Z=(γP0/jωV)×(1−ε(1−j))  (1)ε=(γ−1)δtS/2V  (2)δt=(2κ/ρωCP)1/2  (3)where P0 is static pressure in the closed space (atmospheric pressure), γ is a specific heat ratio of gas (approximately 1.4 in the case of air), V is capacity of the closed space, S is a total surface area in the closed space, ω is an angular frequency of capacity changes (sound), κ is heat conductivity of air, ρ is density of air, CP is specific heat at constant pressure, δt is thickness of a thermal boundary layer, and j is the imaginary unit. It can be seen from Equation (2) that ε which represents effect of δt (thermal boundary layer) on acoustic impedance is proportional to the surface area S.
Also, as can be seen from Equation (1), the acoustic impedance Z varies linearly in the complex plane with changes in the surface area S when the capacity V is constant, and a measurement method is known which removes the effect of the surface area using this relationship (see, for example, patent document 2).
[Patent document 1] Japanese Patent Laid-Open No. 2002-131111
[Patent document 2] Japanese Patent Laid-Open No. 2006-284473
[Patent document 3] Japanese Patent Laid-Open No. 10-300551
However, Equation (1) is an approximate expression in which higher-order terms of the reciprocal of acoustic admittance are omitted by assuming in the process of derivation of Equation (1) that ε is sufficiently smaller than 1. (See “Surface Area Measurement Utilizing Sound,” Torigoe & Ishii, Collected Papers of the Society of Instrument and Control Engineers, Vol. 34, No. 3, 182-187, 1998)
That is, capacity and volume are measured with the effect of the surface area removed by assuming that in the complex plane which represents acoustic impedance, the acoustic impedance varies approximately linearly with changes in the surface area. When no approximation is used, Equation (1) is replaced by Equation (4) below.
[Formula 2]Z=(γP0/jωV)/(1+ε(1−j))  (4)
According to Equation (4), in the complex plane which represents the acoustic impedance Z, the acoustic impedance does not vary linearly with changes in the surface area when the volume is constant. If the effect of the surface area is removed by assuming a linear variation, errors can occur in measurement results.